Question

Xét dấu biểu thức : f(x) = (1-x)(-x\(^2\)+4x-8)

LM GIÙM MK VS NHA

Answer 1

\(f\left(x\right)=\left(1-x\right)\left(-x^2+4x-8\right)\)

ta có : \(-x^2+4x-8=-\left(x^2-4x+8\right)=-\left(x^2-4x+4+4\right)\)

\(=-\left[\left(x-2\right)^2+4\right]=-\left(x-2\right)^2-4\le-4< 0\forall x\)

\(\Rightarrow\) \(f\left(x\right)=0\Leftrightarrow1-x=0\Leftrightarrow x=1\)

\(f\left(x\right)>0\Leftrightarrow1-x< 0\Leftrightarrow x>1\)

\(f\left(x\right)< 0\Leftrightarrow1-x>0\Leftrightarrow x< 1\)

vậy ...........................................................................................